Thermodynamics of MHD flows with axial symmetry

Details Thermodynamics of MHD flows with axial symmetry Thermodynamics of MHD flows with axial symmetry

2004-07-05

arxiv.org/abs/physics/0407025v1

Physical Review E 71 (2005) 036311

Physics

Fluid Dynamics

Scientific paper

10.1103/PhysRevE.71.036311

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation.

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